I’ve simplified my training to something similar than what is outlined in this article, as follows:

Day 1: deadlift variation superset with over head press variation
Day 2: squat variation superset with bench press or dips
Day 3: Repeat day 1
Rest one day when I feel beat up (usually after 3 training days)
Train 5 or 6 days each week.

Progression is simple:
Do reps, not sets; i.e.do as many sets as needed to get 40 reps on the movement (25 reps on the deadlift variations).
Increase weight by 5kg when I can hit 40 reps in 5 sets (25 reps for deadlifts)
Reduce weight by 3kg if I cannot get 40 reps in 10 sets (25 reps for deadlifts)

I do body weight pull ups, push ups and squats every day as part of my general warm up.
For conditioning purposes I only rest 60 seconds between my sets so heart rate is always elevated for the entire workout and I finish with 10 minutes HIT.

I prioritise recovery even though I train almost every day:

My diet is very good

I sleep 7+ hours each night

I never train to failure. My sets stop when the reps noticeably slow down;

I train this way because:
(1) I enjoy it; and
(2) I’m busy and need to be in and out of the gym - this takes less than an hour (40 minutes incl. warm up if I need to drop the conditioning)

Thanks for reading the background. Now for the questions…
(1) I have a nagging concern that performing a squat or a deadlift every day will eventually cause me problems (probably knee joints). I can’t find any program or trainer that recommends this type of structure. Do you think I might be taking too big a risk?
(2) My squat revolves between low bar back, front squat and machine hack squat on each squat day and snatch grip deadlift (from low blocks), sumo and conventional deadlifts on each deadlift day. Do you think there might be noticeable strength improvements from spending one month on one movement and then moving on to another movement for a further month rather than changing every training day?

Depends how new you are and how much weight you’re moving. Myself I can only deadlift heavy once a week but I can squat everyday but everyday isn’t a max out set. First day may be low bar the next is high and fronts they are interchangeable I only lowbar once a week though

I am wondering how the weights are structured. Do you ramp up to a heavy weight, or do 40 reps with a straight weight? Or what do you do?
Because at 40 reps straight weight, I can’t see you get above 50% to 60% intensity (especially when quitting when fatigue starts setting in, as you mentioned).

And adding 5 kg, that’s about 12 lbs for yanks. That is quite some weight, although your lifting numbers show their should be room to go (not trying to be a douchebag!).
adding 2/2,5 kg seems more reasonable for the long term progression (and you train so frequently, you have a lot of opportunities to add weight.)

Adding 5kg is a big jump. I did it on purpose to add phasing into the routine… At 40 reps I consider the benefit to be primarily hypertrophy with strength benefiting to a lesser extent. Add 5kg and my reps go right down and the benefits reverse.

You’re right I have some way to go. If I can ensure proper recovery I hope to be deadlifting and squatting twice body weight within 2 years…